منابع مشابه
Highly connected monochromatic subgraphs
We conjecture that for n> 4(k−1) every 2-coloring of the edges of the complete graphKn contains a k-connectedmonochromatic subgraph with at least n − 2(k − 1) vertices. This conjecture, if true, is best possible. Here we prove it for k = 2, and show how to reduce it to the case n< 7k − 6. We prove the following result as well: for n> 16k every 2-colored Kn contains a k-connected monochromatic s...
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We consider the following question of Bollobás: given an r-colouring of E(Kn), how large a k-connected subgraph can we find using at most s colours? We provide a partial solution to this problem when s = 1 (and n is not too small), showing that when r = 2 the answer is n−2k+2, when r = 3 the answer is ⌊n−k 2 ⌋+1 or ⌈n−k 2 ⌉ + 1, and when r − 1 is a prime power then the answer lies between n r−1...
متن کاملForcing highly connected subgraphs
By a theorem of Mader [5], highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. Solving a problem of Diestel [2], we extend this result to infinite graphs. Here, it is necessary to require not only high degree for the vertices but also high vertex-degree (or multiplicity) for the ends of the graph, i.e. a large number of disjoint rays in each end. We give...
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A popular way of formalizing clusters in networks are highly connected subgraphs, that is, subgraphs of k vertices that have edge connectivity larger than k/2 (equivalently, minimum degree larger than k/2). We examine the computational complexity of finding highly connected subgraphs. We show that the problem is NP-hard. Thus, we explore possible parameterizations, such as the solution size, nu...
متن کاملNote on Highly Connected Monochromatic Subgraphs in 2-Colored Complete Graphs
In this note, we improve upon some recent results concerning the existence of large monochromatic, highly connected subgraphs in a 2-coloring of a complete graph. In particular, we show that if n ≥ 6.5(k − 1), then in any 2-coloring of the edges of Kn, there exists a monochromatic k-connected subgraph of order at least n−2(k−1). Our result improves upon several recent results by a variety of au...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.01.030